HCF of 63, 81, 108, 120 using Euclid's algorithm

Below detailed show work will make you learn how to find HCF of 63,81,108,120 using the Euclidean division algorithm. So, follow the step by step explanation & check the answer for HCF(63,81,108,120).

Here 81 is greater than 63

Now, consider the largest number as 'a' from the given number ie., 81 and 63 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 81 > 63, we apply the division lemma to 81 and 63, to get

81 = 63 x 1 + 18

Step 2: Since the reminder 63 ≠ 0, we apply division lemma to 18 and 63, to get

63 = 18 x 3 + 9

Step 3: We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get

18 = 9 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 63 and 81 is 9

Notice that 9 = HCF(18,9) = HCF(63,18) = HCF(81,63) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 108 is greater than 9

Now, consider the largest number as 'a' from the given number ie., 108 and 9 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 108 > 9, we apply the division lemma to 108 and 9, to get

108 = 9 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 9 and 108 is 9

Notice that 9 = HCF(108,9) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Here 120 is greater than 9

Now, consider the largest number as 'a' from the given number ie., 120 and 9 satisfy Euclid's division lemma statement a = bq + r where 0 ≤ r < b

Step 1: Since 120 > 9, we apply the division lemma to 120 and 9, to get

120 = 9 x 13 + 3

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 9 and 120 is 3

Notice that 3 = HCF(9,3) = HCF(120,9) .

Therefore, HCF of 63,81,108,120 using Euclid's division lemma is 3.